Monotone Jacobi parameters and non-Szego weights

JOURNAL OF APPROXIMATION THEORY

卷:157

Article

Kreimer, Yury²  Last, Yoram²  Simon, Barry¹ 

[1] CALTECH, Pasadena, CA 91125 USA

[2] Hebrew Univ Jerusalem, Inst Math, IL-91904 Jerusalem, Israel

关键词: Orthogonal polynomials;    Schrodinger operators;    Spectral weights;    Szego condition;   

DOI  :  10.1016/j.jat.2008.04.020

来源: Elsevier

【 摘 要 】

We relate asymptotics of Jacobi parameters to asymptotics of the spectral weights near the edges. Typical of our results is that for a(n) 1, b(n) = -Cn(-beta) (0 < beta < 2/3), one has d mu(x) = w(x)dx on (-2,2), and near x = 2, w(x) = e(-2Q(x)) where Q(x) = beta C--1(1/beta) Gamma(3/2)Gamma(1/beta-1/2)(2-x)(1/2-1/beta)/Gamma(1/beta + 1) (1 + O((2-x))). (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

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